Recursion vs Dynamic Programming: How to Identify the Right Approach

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When solving coding problems, one of the most common confusions is whether a problem should be solved using recursion, backtracking, or dynamic programming (DP). Let’s break this down in a structured way so you can quickly identify the right approach during interviews or practice sessions.

πŸ”‘ Step 1: Core Difference​

  • Recursion β†’ Solves a problem by breaking it into smaller subproblems, each solved independently.

  • Dynamic Programming (DP) β†’ A type of recursion where:
    • Subproblems overlap (they repeat).
    • The problem has optimal substructure (optimal solution depends on optimal solutions of subproblems).

πŸ‘‰ Every DP is recursion + memoization/tabulation, but not every recursion is DP.

πŸ”‘ Step 2: Checklist – Is it DP?​


Ask yourself:


  1. Can the problem be expressed recursively?
    Example: Fib(n) = Fib(n-1) + Fib(n-2)


  2. Do subproblems repeat? (Overlapping subproblems)
    Example: Fib(5) calls Fib(4) and Fib(3), but Fib(4) again calls Fib(3) β†’ repetition.


  3. Does it have optimal substructure?
    Example: Knapsack, LIS, shortest paths β†’ best solution depends on smaller optimal solutions.

πŸ‘‰ If only (1) β†’ use recursion.
πŸ‘‰ If (1) + (2) + (3) β†’ use DP.

πŸ”‘ Step 3: Quick Heuristics​

Problems usually solved with Recursion:​

  • Tree traversal (inorder, preorder, postorder)
  • Backtracking (N-Queens, permutations, subsets)
  • Divide & Conquer (merge sort, quick sort, binary search)
  • Unique subproblems (no repetition)

Problems usually solved with DP:​

  • Fibonacci, Climbing Stairs
  • Subset Sum, Knapsack, Partition problems
  • Longest Common Subsequence (LCS), Edit Distance
  • Grid path problems (unique paths, min path sum)
  • Count / Min / Max / True-False optimization problems

πŸ”‘ Step 4: Example Comparison​

Example 1: Fibonacci​

  • Recursive definition: Fib(n) = Fib(n-1) + Fib(n-2)
  • Problem: Fib(3) is computed multiple times β†’ overlapping subproblems.
  • βœ… Use DP.

Example 2: Tree Traversal​

  • Recursive definition: visit left β†’ visit node β†’ visit right.
  • Subproblems are unique, no overlap.
  • ❌ DP not needed.

πŸ”‘ Step 5: Mental Flow​


When you see a problem:

  1. Can I define it recursively? β†’ If no, not recursion/DP.
  2. Am I recomputing the same subproblems? β†’ If yes, move to DP.
  3. Is the problem about optimizing (min/max/count)? β†’ Likely DP.

⚑ Rule of Thumb​

  • Exploring possibilities without repetition β†’ Recursion / Backtracking.
  • Optimizing or counting with overlapping subproblems β†’ Dynamic Programming.

πŸ“ Quick Decision Tree​


Code: 
Problem β†’ Can it be recursive?
          ↓ Yes
    Are subproblems overlapping? β†’ No β†’ Use Recursion/Backtracking
          ↓ Yes
    Does it have optimal substructure? β†’ Yes β†’ Use DP

🎯 Final Words​


Being able to identify recursion vs DP comes with practice. Start with recursion, watch for repeated subproblems, and if you see themβ€”upgrade to DP. In interviews, explicitly state your thought process; it shows depth of understanding even if the final code is not optimal.

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